Honestly? This is a problem with the way your league has been set up, and could probably be taken advantage of EVERY week, not just ASG Week.
A typical 5x5 league (R,HR,SB,RBI,AVG/W,K,SV,ERA,WHIP) has 3 average categories and 7 total categories, encouraging more play (as opposed to better play), especially on the offensive side. Thirty percent of the overall "score" is quality, as opposed to quantity.
By changing those categories in a 6x6 league to include 5 average categories (OBP,SLG,ERA,WHIP,K/9) and 1 negative category (L), your commish has actually inadvertantly encouraged less play, in favor of higher quality play. Unless he's set the minimum innings pitched much higher than the default, this is a very exploitable problem with this league. He's ballooned the quality/quantity numbers up to 50%.
In a league like this, a pitching staff consisting of only four or five premium closers would completely dominate five of the six pitching categories and still not be "punting" wins.
In fact, even after the draft has taken place and all of the closers are taken, you could still exploit this league by trading two or three good starters for another closer and then picking up a couple of top-tier MRs. As long as you've got three closers and two setup guys, you'll still get up near 12-15 innings per week. If you're in danger of missing the minimum by the end of the week you just pick up a spot starter and hope they don't kill your averages. Even if the minimum IP is 20 in a week you could still exploit this by having only two very good starters on your team and trading away the rest for closers and MR.
Not bush-league at all. This is something you should probably have been doing all year. Being aware of league scoring and finding the loopholes is generally how you win leagues, especially leagues like this. Hell, it's the entire story of the season in Fantasy Football! Owners who complain about other owners using strategies like this generally are more upset that they didn't think of it first, or that their teams aren't set up to properly exploit things like this. You can bet that if they were the ones doing it they wouldn't be complaining.